Convolution and Correlation

Summary

The three most often used operations in digital signal processing are convolution, correlation, and the discrete Fourier transform (DFT). In the case of convolution, one of the two sequences is time reversed, whereas no time reversal is required in the computation of correlation. The convolution operation without time reversal is the correlation operation. Correlation operation is used in finding the coefficients of the frequency components of a signal from its amplitude profile in Fourier analysis. Similar to the use of the convolution in the discrete wavelet transform (DWT), correlation operation is also used with double shifts of the data after the computation of each output value. Convolution and correlation are of fundamental importance in both time‐domain and frequency‐domain analysis of signals and systems. Correlation can be implemented by convolution with one of the two signals time reversed. The basic definitions of convolution and correlation are slightly modified in DWT usage.